Essay on Traffic Model
They will be required to solve systems continually based on the following premise: If traffic is to keep moving, during any period of time the number of cars entering an intersection must equal the number of cars leaving that intersection. Let’s see what this means by looking at the intersections of four one-way city streets.
Figure 6.3shows the intersections of four one-way streets.As you study the figure,notice that 300 cars per hour want to enter intersection from the north on 27th Avenue.Also,
200 cars per hour want to head east from intersection on Palm Drive. The letters and stand for the number of cars passing between the …show more content…
The system of equations that models this situation is given by
b. To solve this system using Gaussian elimination, we begin with the augmented matrix. d w + z = 1000 w + x = 1100 x + y = 700 y + z = 600.
System of Linear Equations
(showing missing variables with 0 coefficients) Augmented Matrix d 1w + 0x + 0y + 1z = 1000
1w + 1x + 0y + 0z = 1100
0w + 1x + 1y + 0z = 700
0w + 0x + 1y + 1z = 600 D
We can now use row operations to obtain the following matrix:
The last row of the matrix shows that the system in the voice balloons has dependent equations and infinitely many solutions. To write the solution set containing these infinitely many solutions, let equal any real number. Use the three equations in the voice balloons to express and in terms of
With arbitrary, the alphabetically ordered solution enables us to express the system’s solution set as
c. We are given that construction limits to 50 cars per hour. Because we substitute 50 for in the system’s ordered solution: